Drinking water, regardless if it is filtered by mankind, is filtered by the ground when it's down where we get the water from. Tap water isn't from surface water, like streams. It's from groundwater, which is quite well filtered by the ground. The only difficulty being that well water can have various mineral tastes to it (iron being the main one) depending where you live. Or, if you're in a city with city water, they tend to put all kinds of chemicals in the water, which can make it bad if the city you're in does too much of that.
That said, if the stream is flowing and I happen to be in a remote area such as in the mountains (not next to a city or any factories or anything like that), then yes, I would be willing to drink the water from the stream.
